A challenging problem of cylindrical geometry by HCR

Geometry Level 5

A circular cylindrical hole of radius $\sqrt{2}\text{ m}$ is made through a solid circular cylinder of radius $2\text{ m}$ such that the longitudinal axes of hole and cylinder are perpendicular to each other (As shown in the typical diagram below). What is the volume (of hole) removed from the large cylinder in $\text{m}^3$ ?

The answer is 23.443808.

1 solution

Christopher Criscitiello
Jul 31, 2018

$\left[V=\int_{-\sqrt{2}}^{\sqrt{2}} \left(\int_{-\sqrt{2-y^2}}^{\sqrt{2-y^2}} \left(\int_{-\sqrt{4-y^2}}^{\sqrt{4-y^2}} 1 \, dx\right) \, dz\right) \, dy=\int_{-\sqrt{2}}^{\sqrt{2}} 4 \sqrt{2-y^2} \sqrt{4-y^2} \, dy=23.4438\right]$

A challenging problem of cylindrical geometry by HCR

The answer is 23.443808.

1 solution

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